Unequal Covariance in Mixture Modelin... PreviousNext
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 Elizabeth Koehler posted on Tuesday, February 01, 2005 - 7:15 pm
I am using four variables to generate a mixture of three normal classes. I recently recieved new data and my old code no longer worked. I have found the correct starting values and can get the model to run. However, once I allow the variances to differ between the classes I get an error regarding the Fisher information matrix.

THE MODEL ESTIMATION DID NOT TERMINATE NORMALLY DUE TO AN ILL-CONDITIONED
FISHER INFORMATION MATRIX. CHANGE YOUR MODEL AND/OR STARTING VALUES.

THE MODEL ESTIMATION DID NOT TERMINATE NORMALLY DUE TO A NON-POSITIVE
DEFINITE FISHER INFORMATION MATRIX. THIS MAY BE DUE TO THE STARTING VALUES
BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE CONDITION
NUMBER IS -0.323D-84.

I have looked over the data and of 548 cases, only 506 have a complete set of four variables. I am wodering is this is my problem and what I should try next. Thanks!
 Linda K. Muthen posted on Wednesday, February 02, 2005 - 1:00 am
The problem is not missing data. It may be that one of your classes is empty or very small. You can try to expand the number of random starts.
 Elizabeth Koehler posted on Monday, May 23, 2005 - 9:14 pm
I have a question regarding the interpretation of the unconstrained variance vs. the constrained variance model. I have successfully fit a two class model both ways(only the variance assumption changes between the two models). While this agreement is nice, there are about 1/4 of my sample who switch classes between the two models. The unconstrained model has a better BIC, log-liklihood and LMR p-value. The constrained model has better entropy. As a result, the constrained results look cleaner when plotted by class(the appearance of two seperate classes was much clearer). Is the differnce in class assignment indicative of anything more than this? I have read that the unconstrained model is more likely to converge to the proper solution, so should I proceed with it even though its not as clean? Do you have any suggestions that can guide choosing between these two models?
 bmuthen posted on Monday, May 23, 2005 - 11:58 pm
One useful thing to do is to run the constrained variance model and use the PLOT command to study the plot of estimated means and observed individual trajectories. The latter are for individuals classified into their most likely class. Looking at the plots for each of your two classes, you can see if the scatter of observed trajectories look like they have similar variation across the classes (as an example, see my Biostatistics article - on the Mplus web site). Since you say that the unconstrained model fits better, the variation is probably different and hence the unconstrained model is more faithful to data - even though the entropy is lower.
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